March 2nd. 1901.111
This letter was penned by a copyist;
there is also a draft (LB 9, 66, Cambridge
University Library).

15, Eaton Place, S.W.

Dear Mr. Poincaré,

I am sorry to say it is too true that there are, as you tell me in
your letter which I have received this morning, several mistakes in
respect to magnitude and to sign in my statements regarding the
nutation which would exist if the earth consisted of a rigid
ellipsoidal shell filled with frictionless liquid.222
Poincaré’s
letter has not been located, such that the precise context of his
remarks remains obscure. Plausibly, Poincaré was motivated to
examine Thomson’s theory of nutation while studying Oskar Backlund’s
calculation of the secular variations of the Earth’s equator due to
secular variations of the ecliptic. On the latter topic, see O. Backlund
to Poincaré, 05.02.1901
(§ 3-1-1).
Ever since 1876 when that statement of results
was published, I have been looking for time to go through the
mathematical work again and publish it.333
W. Thomson
1863,
1867, §§ 878–879),
later corrected (W. Thomson 1876), and reedited with minor
changes (W. Thomson
1882, Volume 3, 312–336). Poincaré’s and Orr’s
remarks are aimed at the 1876 version. If I had succeeded in
finding the time, no doubt I would have corrected the errors myself;
but in this I was anticipated by an Irish professor (W.J. Mc. F. Orr,
of the Royal College of Science, Dublin), in a paper published in the
Philosophical Magazine for December
1898.444
Orr 1898. William McFadden Orr (1866–1934),
professor of applied mathematics. The corrections which you will
find in this paper agree, I believe, with those you now give me. The
subject is most interesting, and I hope yet to return to it, but
meantime I hope you will publish your own work with your corrections
of my errors.555
The fact that Poincaré did not publish his corrections of
Thomson’s calculation suggests that they agreed
with those published by Orr (1898).

In my mathematical work I suppose for simplicity the ideal interior
liquid to be frictionless. No assumption of viscosity in the liquid
would be, to my mind, very interesting. It certainly could not show
any way of escaping my main conclusion that the earth is on the whole
an elastic solid of high rigidity; though probably or possibly not so
high as to cause practically perfect resistance against change of
shape by the tide-generating influences of the sun and moon.

I thank you warmly for your kindness in writing to me and telling me
of the errors you have found.

W. Thomson (1863)On the rigidity of the earth; shiftings of the earth’s instantaneous axis of rotation; and irregularities of the earth as a timekeeper.
Philosophical Transactions of the Royal Society of London153, pp. 573–582.
Cited by: footnote 3.